A047085 a(n) = T(2*n, n), array T as in A047080.

1, 1, 3, 9, 27, 83, 259, 817, 2599, 8323, 26797, 86659, 281287, 915907, 2990383, 9786369, 32092959, 105435607, 346950321, 1143342603, 3772698725, 12463525229, 41218894577, 136451431723, 452116980643, 1499282161375, 4975631425581, 16524213199923, 54913514061867

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

From G. C. Greubel, Oct 30 2022: (Start)

a(n) = A171155(n).

G.f.: sqrt((1 - x)/(1 - 3*x - x^2 - x^3)). (End)

D-finite with recurrence n*a(n) +(-4*n+3)*a(n-1) +(2*n-5)*a(n-2) -a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Oct 22 2025

Mathematica

CoefficientList[Series[Sqrt[(1-x)/(1-3*x-x^2-x^3)], {x, 0, 50}], x] (* G. C. Greubel, Oct 30 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 50); Coefficients(R!( Sqrt((1-x)/(1 -3*x-x^2-x^3)) )); // G. C. Greubel, Oct 30 2022
(SageMath)
def A047085_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( sqrt((1-x)/(1-3*x-x^2-x^3)) ).list()
A047085_list(50) # G. C. Greubel, Oct 30 2022

Crossrefs

Cf. A047080, A047081, A047082, A047083, A047084, A047086, A047087, A047088.

Cf. A171155 (duplicate of this sequence; see there for more information).

Sequence in context: A099786 A237272 A192909 * A171155 A131428 A099787

Adjacent sequences: A047082 A047083 A047084 * A047086 A047087 A047088

Keyword

nonn

Author

Clark Kimberling

Extensions

Data corrected by Sean A. Irvine, May 11 2021

Status

approved